H is the Hamiltonian. Here we set µ=0. For grand-canonical calculations add -6µ to the main diagonal.

2*U	0	0	0	0	0	-(Sqrt[2]*t)	2*t
0	2*U	-2*t	0	0	Sqrt[2]*t	0	-(Sqrt[2]*t)
0	-2*t	2*U	Sqrt[2]*t	t	0	0	0
0	0	Sqrt[2]*t	2*U	0	0	-(Sqrt[2]*t)	0
0	0	t	0	U	-(Sqrt[2]*t)	-2*t	0
0	Sqrt[2]*t	0	0	-(Sqrt[2]*t)	U	0	0
-(Sqrt[2]*t)	0	0	-(Sqrt[2]*t)	-2*t	0	U	0
2*t	-(Sqrt[2]*t)	0	0	0	0	0	U